### Abstract

We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period L. FPT statistics are crucially affected by the disorder realization. In the large-L limit, we obtain exact formulas for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulas are still useful for nonperiodic heterogeneous environments; i.e., the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.

Original language | English |
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Article number | 052127 |

Journal | Physical Review E |

Volume | 99 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2019 May 20 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E*,

*99*(5), [052127]. https://doi.org/10.1103/PhysRevE.99.052127

**Exact results for first-passage-time statistics in biased quenched trap models.** / Akimoto, Takuma; Saitou, Keiji.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 99, no. 5, 052127. https://doi.org/10.1103/PhysRevE.99.052127

}

TY - JOUR

T1 - Exact results for first-passage-time statistics in biased quenched trap models

AU - Akimoto, Takuma

AU - Saitou, Keiji

PY - 2019/5/20

Y1 - 2019/5/20

N2 - We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period L. FPT statistics are crucially affected by the disorder realization. In the large-L limit, we obtain exact formulas for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulas are still useful for nonperiodic heterogeneous environments; i.e., the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.

AB - We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period L. FPT statistics are crucially affected by the disorder realization. In the large-L limit, we obtain exact formulas for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulas are still useful for nonperiodic heterogeneous environments; i.e., the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.

UR - http://www.scopus.com/inward/record.url?scp=85066754717&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066754717&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.99.052127

DO - 10.1103/PhysRevE.99.052127

M3 - Article

C2 - 31212478

AN - SCOPUS:85066754717

VL - 99

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 5

M1 - 052127

ER -